{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "22f037ad-d2ec-485a-9798-9ac8bf350480",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "# Anscombe's Quartet\n",
    "\n",
    "The raw data has four series. The correlation coefficients are high.\n",
    "Visualization shows that a simple linear regression model is misleading.\n",
    "\n",
    "## Raw Data for the Series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a79d2991-7893-4cb2-b001-b55888c68efc",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import json\n",
    "from pathlib import Path\n",
    "import statistics\n",
    "\n",
    "from pydantic import BaseModel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "99a55c73-67ad-4ce0-9faf-7921a179e5f2",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "class Pair(BaseModel):\n",
    "    x: float\n",
    "    y: float\n",
    "\n",
    "class Series(BaseModel):\n",
    "    series: str\n",
    "    data: list[Pair]\n",
    "\n",
    "    @property\n",
    "    def x(self) -> list[float]:\n",
    "        return [p.x for p in self.data]\n",
    "        \n",
    "    @property\n",
    "    def y(self) -> list[float]:\n",
    "        return [p.y for p in self.data]\n",
    "\n",
    "    @property\n",
    "    def correlation(self) -> float:\n",
    "        return statistics.correlation(self.x, self.y)\n",
    "\n",
    "    @property\n",
    "    def regression(self) -> tuple[float, float]:\n",
    "        return statistics.linear_regression(self.x, self.y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "9f5030f1-f7bb-4254-a829-86cf198eed9c",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "source = Path.cwd().parent.parent / \"data\" / \"anscombe.json\"\n",
    "with source.open() as source_file:\n",
    "    json_document = json.load(source_file)\n",
    "    source_data = (Series.model_validate(s) for s in json_document)\n",
    "    quartet = {s.series: s for s in source_data}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "df4a3189-55df-42f0-ad86-0b61e41cedba",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Series(series='I', data=[Pair(x=10.0, y=8.04), Pair(x=8.0, y=6.95), Pair(x=13.0, y=7.58), Pair(x=9.0, y=8.81), Pair(x=11.0, y=8.33), Pair(x=14.0, y=9.96), Pair(x=6.0, y=7.24), Pair(x=4.0, y=4.26), Pair(x=12.0, y=10.84), Pair(x=7.0, y=4.82), Pair(x=5.0, y=5.68)])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quartet['I']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "13108efb-7c10-4250-8c24-4bff9d53f66c",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Series(series='IV', data=[Pair(x=8.0, y=6.58), Pair(x=8.0, y=5.76), Pair(x=8.0, y=7.71), Pair(x=8.0, y=8.84), Pair(x=8.0, y=8.47), Pair(x=8.0, y=7.04), Pair(x=8.0, y=5.25), Pair(x=19.0, y=12.5), Pair(x=8.0, y=5.56), Pair(x=8.0, y=7.91), Pair(x=8.0, y=6.89)])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quartet['IV']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c381c215-048e-4534-88a2-0c8818efd0ae",
   "metadata": {},
   "source": [
    "## Statistical Computations\n",
    "\n",
    "Two properties compute correlation coefficient, $r$, and perform linear regression.\n",
    "The regression gives us two parameters for a line.\n",
    "- Slope, $m$.\n",
    "- Intercept, $b$.\n",
    "\n",
    "The equation is $y = m \\times x + b$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5b3ae023-bcf4-43cb-9444-692174a58e76",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.81642051634484"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quartet['I'].correlation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "e67f9021-f8c0-4ff9-a42a-cc11f251131d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'y = 0.5 * x + 3.0'"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = quartet['I'].regression\n",
    "f\"y = {r.slope:.1f} * x + {r.intercept:.1f}\""
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b7d5caf7-dedf-4bed-8cf3-f482de21e302",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "source": [
    "## Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "512046c8-a3a7-43dc-9f70-456835485651",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e996d383-57ce-4616-8d2a-8e5023780d20",
   "metadata": {
    "editable": true,
    "slideshow": {
     "slide_type": ""
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(layout='tight')\n",
    "ax_dict = fig.subplot_mosaic(\n",
    "    [\n",
    "        [\"I\", \"II\"],\n",
    "        [\"III\", \"IV\"],\n",
    "    ],\n",
    ")\n",
    "for name, ax in ax_dict.items():\n",
    "    series = quartet[name]\n",
    "    ax.scatter(series.x, series.y)\n",
    "    ax.set_title(f\"Series {name}\")\n",
    "    lr = series.regression\n",
    "    eq1 = rf\"$r = {series.correlation:.3f}$\"\n",
    "    eq2 = rf\"$Y = {lr.slope:.1f} \\times X + {lr.intercept:.2f}$\"\n",
    "    ax.text(.95, .05, f\"{eq1}\\n{eq2}\",\n",
    "            fontfamily='sans-serif',\n",
    "            horizontalalignment='right', verticalalignment='bottom', transform=ax.transAxes)\n",
    "    ax.axline((0, lr.intercept), slope=lr.slope)\n",
    "plt.show()"
   ]
  },
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